by Aaron Sandlin | Aug 4, 2015 | Math
Break out of your cage!
Forget about the lines that have been placed around the equation in your mind! They aren’t real! You may have been taught a certain formula or equation that you hold sacred in your belief in the immutable structure of math. Please, do away with these structures that hold you tight. The only things that are not fluid in math are the basic rules; the properties inherently found. These are things like the commutative property, where two plus five equals five plus two and so on. The majority of mathematical discovery has been the result of people willing to play around with a known equation.
For example, the law of cosines is able to be turned into the dot product of vectors. These two formulas are separated in instruction by different classes; trigonometry and calculus 3, respectively. However they are really separated only by a little algebraic manipulation.
“The definition of the dot product incorporates the law of cosines, so that the length of the vector from X to Y is given by
|X-Y|^2 = (X-Y)·(X-Y)
= X·X-2X·Y+Y·Y
= |X|^2+|Y|^2-2|X||Y|cos(θ),
where θ is the angle between X and Y.”
~https://mathworld.wolfram.com/LawofCosines.html
We are taught to stay on the path that has been built by centuries of achievement prior to our instruction, but all of that achievement was accomplished exactly by people who wandered off of the beaten path. If you want to learn all that there has already been discovered, then by all means stay in your predetermined path. It is much safer there. If you want to truly discover the full power of math, though, then let your mind become fluid, only allowing the basic laws of mathematical nature to be your bounds. This is the difference between a painter and an artist. Even if you do not become the next Rembrandt and your work looks more like Picasso’s, you will have done one seemingly small but immensely important thing: You allowed yourself to question, to explore, to have a brain that sees things in a scientific light.
If you never discover a formula for anything new under the sun, you might, through the mere fact of having developed an inquisitive mind, have allowed yourself to see EVERYTHING in that same fluid manner. Art, business, sports, tactics, law, medicine….the sky is the limit.
See, math isn’t just for counting; Math is for THINKING and in a manner that literally restructures one’s mind to see all of the universe in a new light. So, cast off those chains of the rigid equations! Play with your numbers! Move things to the “wrong” side of that equal sign! Remake your mind.
by Aaron Sandlin | Mar 2, 2015 | Math, Teaching and Learning
One of my math professors always insisted on showing us around thirty minutes of why a concept works and how to get the formula that we use in the final product. Once he showed us the short cut (formula) the work went from ten minutes of calculating to ten seconds. Back then everyone groaned about the “waste of time” but now that we are free of his tyranny, we are coming into contact with the “formula people”. They are the folk who panic every time they have to use an old concept in a new way. Why are they so unsure? It is because they were told to take the math on faith. They were taught that “It just works” and that was okay for them. My math mentor would routinely go through some fake absurd process on the board and watch the majority of the room follow his false trail. He awarded bonus points to anyone who rightfully challenged him by understanding the concept and working it out for yourself. The sad thing is that for my entire education until now the teachers taught instead of mentored.
It wasn’t until I was 29 yrs. old that I finally experienced why any number raised to the zero exponent is one. See my short video explanation, Powers of 0 and 1. I had been told that it was one and sent on my way, just relying on my memory to retain that knowledge. After a long gap in school between high school and college, I had forgotten even that simple rule. I have often heard that math is not like riding a bike and I have said it myself. You have to keep it up or the knowledge melts away. Could we be wrong? When I think back to my trigonometric identities, I can’t remember them! BUT, I remember one concept that was experienced and I can reliably derive the rest of the identities from that one branch. Think about bikes for a minute. Did you get tested on the methods of balance? Were you drilled on the names of a bicycles parts and their purposes? Was everyone made to ride on standardized bikes and had to all learn at the same pace? Do you recall the physics class you had to pass in order to take your training wheels off? How is it that just about anyone who ever learned the difficult task of riding a bike can go for years without practice and still retain the skill? It is because we all experienced the process of learning instead of memorizing the concept. I bet a shiny nickel that anyone who had never learned how to ride a bike, but had studied it in a book, would not remember the necessary information needed to describe the process to someone else. Years ago I had memorized the algorithm for solving a Rubiks Cube. Give me one today and I can’t do it! I failed to develop the fundamental experience necessary to achieve mastery of that skill. If you want to learn mathematics instead of memorize formulas, you need to know the why that sadly is too often left out in s foolhardy quest for time and effort savings. So the next time a “teacher” asks you to memorize a formula, be brave, and ask “why?” and turn them into a mentor.
by Aaron Sandlin | Jan 19, 2015 | Math
Thinking de about a career in mathematics may lead some people to think only of math and leave out the other three fields empresa in which math is a cheap mlb jerseys critical player. These fields are science, technology, engineering and mathematics and they are acronated as the word STEM. All of the hundreds of careers that fall under the STEM banner are How laid on wholesale nba jerseys the foundation of fotograflar? mathematics. I want to become an electrical engineer Vision and then progress towards quantum physics with a research scientist career for cheap jerseys government research facility such as NASA, the National Aeronautical Space Agency, or cheap nfl jerseys for Prepare a university like the Georgia Institute of Technology.
Everyone that wants to advance our understanding of the universe, or find a faster or cheaper way to manufacture Slinkys must still study math first. If you want to be the person to find a way to verbally communicate with dolphins, first you must know math. If you want to be a financial professional like an accountant, actuary or market analyst, first you must know math. Math is the concrete that we build all manner of buildings upon. Yes, mathematics can be difficult at times, but that is it’s strength. Anything that is built on something easy will not stand against something hard. Any job you can think of as part of a business or field that has been developed or is maintained by people who have the strong concrete foundation of math. Do you work at McDonald’s? Someone used math to find out how to efficiently feed millions of people in a way that is predictable, enjoyable, and not costly. Are you a game warden? Someone used math to map migration paths for the animals you need to be protecting and they used mathematical population growth models to determine how many hunting licenses to issue which fund your position. Geologists might even save your life by using math to correctly predict and warn of a volcanic eruption in your park. Are you a truck driver? Without engineers designing strong bridges to open up more shipping routes or more fuel efficient trucks, your company would not have the ability to hire as many drivers. Can you see how valuable someone skilled in math is to all of those who are employed in various fields? That value comes with a hefty price tag. The skills of those well versed in mathematics are in short supply and the demand is strong and in every corner of the economy.
